As I had to correct my own post over this issue, I thought I’d share it. In this case, years is possessive, so it should be 15 years’ experience.

Here are some more examples:The company owed me a day’s pay – apostrophe before the s as it’s just one day.The company owed me three days’ pay (apostrophe after the s as it’s more than one day).The same applies below:He has a year’s experience as a teacher.He has three years’ experience as a teacher.

Photo credit: Wikipedia

Here is an exception: The plural of millennium (1,000 years) is millennia (not millenniums).So – China has three millennia of history – you can’t say millennias, because millennia is already plural, and an apostrophe just doesn’t fit.
Of course, you can get around this problem by simply saying:China has three-thousand years’ history – orChina has a three-thousand-year history – orChina has three-thousand years of history